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Subject Mathematics Geometry Total 68 hoursKazakh-American University Subject Mathematics Geometry Total 68 hours Theme of the lecture Quadrilateral 2 hours/ week Lecturer Grachyova Svetlana Semenovna. Profile Economics Grade 8 Academic year 2014-2015 1 term Lesson 5
Definition: Quadrilateral is a figure, which consists of four point and four segments joint consequently. Four points don’t belong to one straight line.
If number of points is more than four- this figure is called polygon.
A, B,C,D- vertexes; AB,BC,CD,AD- sides; AB, CD and AD,BC-opposite sides; AB, BC and BC,CD and CD,AD and AD,AB-adjacent sides; A, B and B,C and C,D and D,A- adjacent vertexes; A, RegularC and B,D- opposite vertexes;
AC and BD- diagonals of quadrilateral. Perimeter of quadrilateral is sum of length of all sides. Quadrilateral divides plane in two parts: interior and exterior. Convex quadrilateral- if each angle is less than two right angles.
Regular or Equilateral quadrilateral – if all sides are equal to each other. Exercises: Prove that some of angles of quadrilateral is equal to 3600
Glossary
Home task Theorem, definitions Lesson 1 ex 28,29, 30 Individual work of student: Collection for preparing to examination Group 15 (15A01 –15A05). Office–hours Geometry 8grade Шыныбеков А.Н. 2011, ex 7 ( p 3-5) Literature: Geometry 8grade Шыныбеков А.Н. 2011, [3 – 5], Collection for preparing to examination Group15 Additional literature Tulebaeva S.K. Geometry . 8 grade. Collections of problems
Notes Kazakh-American University Subject Mathematics Geometry Total 68 hours Theme of the lecture Parallelogram 2 hours/ week Lecturer Grachyova Svetlana Semenovna. Profile Economics Grade 8 Academic year 2014-2015 1 term Lesson 6-8 Definition Two segments are called parallel if they belong to parallel lines.
Definition Parallelogram – quadrilateral in which opposite sides are parallel
Tests for parallelogram 1. Opposite sides are equal
2. Point of crossing of diagonals divides them in half
3. Opposite side are parallel and equal
Theorem
If two opposite sides of quadrilateral are equal and parallel, this quadrilateral is parallelogram
Theorem
If opposite angles of quadrilateral are equal then this quadrilateral is parallelogram
Theorem
If point of crossing of diagonals of quadrilateral divides them in half, then this quadrilateral is parallelogram
Answer Questions and explain
1. How many questions is it possible to construct using two equilateral triangles
2. How many questions is it possible to construct using two isosceles triangles
3. How many questions is it possible to construct using two arbitrary triangles
Glossary
Home task: Parallelogram Lesson 1 ex 53, 54. Lesson 2 ex 57, 59 Lesson 3 ex 62, 63 Individual work of student: Collection for preparing to examination Group 15 (15A06 –15A10). Office–hours Geometry 8grade Шыныбеков А.Н. 2012, ex 11, 20 ( p 5-8) Literature: Geometry 8grade Шыныбеков А.Н. 2012, [5- 8], Collection for preparing to examination Group15 Additional literature Tulebaeva S.K. Geometry . 8 grade. Collections of problems
Notes Kazakh-American University Subject Mathematics Geometry Total 68 hours Theme of the lecture Rectangle 2 hours/ week Lecturer Grachyova Svetlana Semenovna. Profile Economics Grade 8 Academic year 2014-2015 1 term Lesson 9 Definition Rectangle - is a quadrilateral in which each angle is equal to right angle. Properties of rectangle Rectangle – is a parallelogram with equal angles. Diagonals of rectangle are equal. Rectangle has all properties of parallelogram. Write all properties of rectangle, using properties of parallelogram.
Glossary
Home task: Rectangle Lesson 1 ex 87, 88
Individual work of student: Collection for preparing to examination Group 15 (15A10 –15A15). Office–hours Geometry 8grade Шыныбеков А.Н. 2011, ex 11, 20 ( p 21-33) Literature: Geometry 8grade Шыныбеков А.Н. 2011, [21 - 33], Collection for preparing to examination Group15 Additional literature Tulebaeva S.K. Geometry . 8 grade. Collections of problems
Notes
Kazakh-American University Subject Mathematics Geometry Total 68 hours Theme of the lecture Rhomb. Square 2 hours/ week Lecturer Grachyova Svetlana Semenovna. Profile Economics Grade 8 Academic year 2014-2015 1 term Lesson 10 – 11 Lesson 12 – Control work Definition Rhomb – is a parallelogram with equal sides Properties of rhomb All side are equal Opposite angles are equal Point of crossing of diagonals divides them in half Diagonals of rhomb are perpendicular to each other Diagonals are bisectors of their angles.
Definition Square – is a rectangle with equal sides Properties of square All sides are equal Each angle is equal to right angle Diagonals are equal Point of crossing of diagonals divides them in half Diagonals are bisectors of each angle Diagonals are perpendicular to each other
Solve problem Find perimeter of rectangle if bisector of angle A divides angle side BC in segments 45,6 cm and 7,885 cm. Glossary
Home task Lesson 1 ex 97, 98 Lesson 2 ex 101, ex 102 Individual work of student: Collection for preparing to examination Group 15 (15A16 –15A20). Office–hours Geometry 8grade Шыныбеков А.Н. 2011, ex 21, 28 ( p 921-33) Literature: Geometry 8grade Becboev Zh, 2012, [21-33], Collection for preparing to examination Group15 Additional literature Tulebaeva S.K. Geometry . 8 grade. Collections of problems 200] Notes Kazakh-American University 12 |
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